17.Two paddocks in the shapes shown below are to be fenced with wire. If the same total
amount of wire is used for each paddock, what are the dimensions of each paddock in
metres?

The solution to each of these recurrence relations with the given initial conditions are a) an = 1+1+2+3+4+5.....+n and b) an = n.n-1.n-2 = 2.5 = (n!)5

In the field of mathematics, a recurrent equation is a formula that determines the nth value of a sequence of numbers based on a combination of previous values. Typically, the equation only involves k past values of the sequence, where k is a constant parameter independent of n; this k is known as the recurrence order. These equations, also known as difference equations, describe a sequence or array in terms of itself through recursion. They establish a relationship between the dependent variable and the differences of various orders of the variable. Recurrent equations can be utilized to model the runtime of recursive programs by distinguishing between recursive and non-recursive operations.

a) an = an-1 + n, ao = 1

a1 = a0 +1 = 1+1

a2 = a1+2 = 1+1+2

a3= a2+3 = 1+1+2+3

an = 1+1+2+3+4+5.....+n

1+n(n+1)/2 = n2+n+2/2

e) an = n an-1, ao = 5

a1 = ao = 5

a2 = 2 a1 = 2.5

a3 = 3 a2 = 3.2.5

an = n.n-1.n-2 = 2.5 = (n!)5

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Answer:

i) 42 candidates passed Mathematics, 33 candidates passed Science.

ii) There is a 75% chance that a candidate passed exactly one subject.

Step-by-step explanation:

So we know that in total there are 60 candidates, and 15 passed both.

That leaves us with 45 candidates that passed either science or math. Since 9 more passed math than science, we see that out of those 45, 27 candidates passed math and 18 passed science. We add the 15 that got through both to each number, which means in total 42 candidates passed Mathematics, 33 candidates passed Science.

To see the probability, we know that 45 out of 60 only passed one subject. Simplified is 3/4 or 75%.

there are 9 office suites in company C and the total number of office suites in the three companies is 75.   To solve this problem, we first need to find out how many office suites company A and company B have. Let's represent the total number of office suites in the three companies as x.

Company A has 1/3 of the computers, which means they have 1/3 of the office suites as well. So the number of office suites in company A is:

1/3 * x = x/3

Company B has 2/5 of the computers, which means they have 2/5 of the office suites as well. So the number of office suites in company B is:

2/5 * x = 2x/5

To find out how many office suites are in company C, we can use the fact that the total number of office suites is 60. So we can write an equation:

x/3 + 2x/5 + C = 60

We can simplify this equation by finding a common denominator for the first two terms:

5x/15 + 6x/15 + C = 60

11x/15 + C = 60

Now we can solve for C by isolating it on one side of the equation:

C = 60 - 11x/15

To find the value of x, we can use the fact that the total number of office suites is 60:

x/3 + 2x/5 + (60 - 11x/15) = 60

Multiplying both sides by 15 to eliminate the denominator, we get:

5x + 6x + 900 - 11x = 900

Simplifying, we get:

x = 75

So the total number of office suites in the three companies is 75. To find out how many are in company C, we can substitute x into the equation we found for C:

C = 60 - 11x/15 = 60 - 11(75)/15 = 9

Therefore, there are 9 office suites in company C.

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There are 60 office suites company a has 1/3 of computers company b has 2/5 of computers how many are in company c buildingservice the computers?

. Company A services the computers at 1/3 of the office suites A.16

. Company B services the computers at 2/5 of the office suites B.20

. Company C services the computers at x of the office suites C. 24

D. 28

Answer:

See attached.

Step-by-step explanation:

Helping in the name of Jesus.

Answer: x = 1 In4

Step-by-step explanation:

Sorry if I’m wrong

This is not a line of best fit because it does not pass through two of the data points. Option D

The line of best fit is a straight line that is used to represent the general trend in a scatter plot or a set of data points. It is also known as the regression line, as it is often used in regression analysis to model the relationship between two variables.

The line of best fit is chosen to minimize the distance between the line and the data points, typically by minimizing the sum of the squared errors (the differences between the actual y-values and the predicted y-values on the line).

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Answer:

-7

Step-by-step explanation:

We dont know the starting temperature so we will just put x for the starting temperature

The temp is first doubled so x*2

Then the temp drops by 10 so 2x-10

After that the temp increases by 40 so 2x-10+40

2x-10+40=16

2x+30=16

2x=16-30

2x=-14

x= -14/2

x=-7

The two lines will be parallel and won't overlap anywhere if they have separate intercepts but the same slope.

given

It appears from the graph that the two lines cross at the location (10, 0). But it's possible that the system has a solution that can't be seen from this part of the coordinate plane.

We would need further information about the slopes and intercepts of the two lines in order to establish whether there is a solution that we cannot see in this region of the coordinate plane.

We have already located the spot on the graph where the two lines will intersect if their slopes and intercepts are different.

The two lines will be parallel and won't overlap anywhere if they have separate intercepts but the same slope.

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Answer:

Since the equation of the circle is:

[tex](x-3)^2 +(y-1)^2 = 100[/tex]

we can conclude that:

1. The center has coordinates (3, 1)

2. The new circle has a center with coordinates (3,5)

3. The new circle has an equation of:

[tex](x -3)^2 +(y - 5)^2 = 100[/tex]

Answer:

height ≈ 17.0 m

Step-by-step explanation:

consider the right triangle with angle 29° , opposite side x and adjacent side of 28 m

using the tangent ratio in the right triangle

tan29° =[tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{x}{28}[/tex] ( multiply both sides by 28 )

28 × tan29° = x , then

x ≈ 15.5 m ( to the nearest tenth )

now add on the 1.5 m

height of tree = 15.5 + 1.5 = 17.0 m

Answer:

[tex]\frac{1}{35}=0.029[/tex]

Step-by-step explanation:

Each marble has a probability  [tex]\frac{1}{7}[/tex]  of being pulled out of the bag.

We need to pull out green, blue, red or yellow in the first pull.

That is mean we have a  [tex]\frac{4}{7}[/tex] probability to choose one of these. (Let it be green marble)

In secend pull we have 6 marbles in the bag and 3 of them we need to pull out. That is meean we have a probability [tex]\frac{3}{6}[/tex] to choose one of these (Let it be blue marble).

In third pull we have 5 marbles in the bag and 2 of them we need to pull out. That is meean we have a probability [tex]\frac{2}{5}[/tex] to choose one of these (Let it be red marble).

In last pull we have 4 marbles in the bag and we need to pull out last one (yellow). That is meean we have a probability  [tex]\frac{1}{4}[/tex].

[tex]\frac{4}{7} *\frac{3}{6} *\frac{2}{5}* \frac{1}{4} =\frac{4}{7} *\frac{1}{2} *\frac{2}{5} *\frac{1}{4} =\frac{1}{35}= 0.029[/tex]

The rectangle ABCD have measures of angle a and b derived to be 69° and 138° respectively to the nearest degree.

Considering the right triangle ADC,

tan ACD = 6/16 {opposite/adjacent}

ACD = tan⁻¹(6/16)

ACD = 20.5560

ACD = 21° to the nearest degree

Angle ACD = Angle ABD, and ABD and a are complementary angles, so;

a + ABD = 90°

a + 21 = 90°

a = 90 - 21

a = 69

The angle b forms an isosceles triangle with the angles C and D, so;

b = 180 - 2(21) {sum of interior angles of a triangle}

b = 180 - 42

b = 138°

Therefore, the rectangle ABCD have measures of angle a and b derived to be 69° and 138° respectively to the nearest degree.

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The height of the main cable 20 meters from the center is 16 meters above the road.

To find the equation of the parabola, we need to use the information given about the height of the cables at the towers and the center of the bridge. We know that the main cables are 20 meters above the road at the towers, so we can use this information to find the distance between the towers, which is

distance between towers = 80 meters - 2(20 meters) = 40 meters

We also know that the main cables are 4 meters above the road at the center, so we can use this information to find the height of the vertex of the parabola, which is

vertex height = 4 meters + 20 meters = 24 meters

We can now use the vertex form of a parabola to write the equation

y = a(x - h)^2 + k

where (h, k) is the vertex and a is a constant that determines the shape of the parabola.

Substituting the values we found for the vertex height and the distance between the towers, we get

y = a(x - 40)^2 + 24

We now need to find the value of a. To do this, we can use the fact that the vertical cables are spaced every 10 meters. This means that the distance between the vertex of the parabola and a point on the main cable 10 meters from the center of the bridge is

distance = 10 meters

Substituting x = 50 (since the center of the bridge is at x = 40 + 10 = 50) and y = 14 (since the cable is 4 meters above the road at this point), we get

14 = a(50 - 40)^2 + 24

-10 = 100a

a = -0.1

Substituting this value of a into the equation we found earlier, we get

y = -0.1(x - 40)^2 + 24

To find the height of the main cable 20 meters from the center, we can substitute x = 60 (since the center of the bridge is at x = 50 and we want to go 20 meters to the right) into the equation

y = -0.1(60 - 40)^2 + 24

y = -0.1(20)^2 + 24

y = -0.1(400) + 24

y = -40 + 24

y = -16

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Answer:

9 boys, 27 girls

Step-by-step explanation:

2 boys : 6 girls = 1 boy : 3 girls

Let b = number of boys and g = number of girls.

[tex] \frac{1}{3} = \frac{b}{g} [/tex]

[tex]g = 3b[/tex]

[tex]b + 3b = 4b = 36[/tex]

[tex]b = 9[/tex]

[tex]g = 27[/tex]

The probability that at least 50 respondents of a random sample of 100 Mississippi residents do not identify themselves as conservative is 0.9989, or approximately 99.89%.

What is binomial distribution?

A binomial distribution is a type of distribution distinct from a continuous distribution in which every trial has an equal chance of reaching a given value and is independent of every other trial. The binary distribution has only two possible outcomes.

This is a binomial distribution problem with n = 100 (sample size) and p = 0.4278 (the probability of not identifying as conservative, which is 1 - 0.572).

The probability of at least 50 respondents not identifying themselves as conservative can be calculated using the cumulative distribution function (CDF) of the binomial distribution:

P(X ≥ 50) = 1 - P(X < 50)

Using a binomial calculator or software, we can find that P(X < 50) = 0.0011.

Therefore,

P(X ≥ 50) = 1 - P(X < 50) = 1 - 0.0011 = 0.9989

So, the probability that at least 50 respondents of a random sample of 100 Mississippi residents do not identify themselves as conservative is 0.9989, or approximately 99.89%.

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Answer:

x=2

Step-by-step explanation:

x=7-5

x=2

Thank you for your question

5(7+y)*z

y = 0.4 and z = 1.6

5(7+y)*z

(35 + 5y)*1.6

[35 + 5(0.4)]*(1.6)

(35 + 2)*1.6

37 * 1.6

59.2

Thus, the answer is a) 59.2

If a shoe size of 8 is added to the data, the IQR is affected in the following way: C. the IQR remains a 2.

In Mathematics, interquartile range (IQR) is the difference between quartile 1 (Q₁) and quartile 3 (Q₃):

IQR = Q₃ - Q₁

Based on the given data set, we can logically deduce the following interquartile ranges:

Quartile 3 (Q₃) = 8

Quartile 1 (Q₁) = 6

Now, the interquartile range (IQR) can be calculated as follows:

Interquartile range (IQR) = Q₃ - Q₁

Interquartile range (IQR) = 8 - 2

Interquartile range (IQR) = 2

Based on the 1.5 × IQR rule for outliers, we have:

1.5 × IQR = 1.5 × 2 = 3

Therefore, the shoe size will be 3 points below Q₁ and 3 points above Q₃:

Lower shoe size = 6 - 3 = 3

Upper shoe size = 8 + 3 = 11.

In conclusion, we can reasonably infer and logically deduce that the interquartile range (IQR) would remain at 2.

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The 55 in the expression represents the speed of the family’s car in miles per hour.

What is called distance?

The complete length of the path between any two points is called distance.

The expression 245-55t represents the distance, in miles, the family still needs to drive after t hours.

A camp counselor starts from home and drives to a campground.

The expression 245-55t represents the distance, in miles, the counselor still needs to drive after t hours.

Now, in expression 245 is the distance in miles between his home to the campground.

And 55 is the rate at which the distance 245 miles is reducing per hour.

The 55 in the expression represents the speed of the family’s car in miles per hour.

If the speed of the camp counselor is 55 miles per hour, then we can use the formula distance = speed × time

 Find out  long it will take for the counselor to reach the campground?

Let’s set distance = 0 and solve for t:

245-5t = 0

55t = 245

t =  4.45hours

Therefore, it will take approximately 4.45 hours for the camp counselor to reach the campground.

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Answer:

Step-by-step explanation:

Answer: 165 square cm

Step-by-step explanation:

Thus, the equation of line  parallel to given line and with passing points (-6, -4) is: y = -1/6 x - 10.

The slopes for perpendicular lines are the opposite reciprocals of the slopes of parallel lines, which are equal. It's a worked example of identifying the parallel or perpendicular nature of given lines.

The standard slope intercept form:

y = mx + c  ..eq 1

slope m and y intercept is c.

Given equation:

y = -1/6 x + 2 ..eq 2 on comparing eq 2 with eq 1

m = -1/6 and c is 2

Now, slope of two parallel lines are same.

Passing point = (-6, -4)

Equation of line:

y - y1 = m (x - x1)

y + 4 = -1/6( x + 6)

y = -1/6 x - 10

Thus, the equation of line  parallel to given line and with passing points (-6, -4) is: y = -1/6 x - 10.

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Part A: The total distance that the both friends covered with their bicycle = 7n + 7

Part B: The difference between the miles ridden by Jackson and the miles ridden by Ayanna would be =n-3.

The distance that was covered by;

Jackson = 4n + 2

Ayanna = 3n + 5

Total distance = 4n + 2+3n + 5

= 7n + 7

The difference between the both distance = (4n + 2)- 3n + 5

= 4n+2-3n-5

= n -3

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The length of the edge of the square is increasing at a rate of 12/13 cm/min when the area is 169 cm^2, given that the area of the square is increasing at a rate of 24 cm^2/min.

Let's assume that the side length of the square is represented by "x" and the area of square is represented by "A". Then we have:

A = x^2

Differentiating both sides with respect to time "t", we get:

dA/dt = 2x(dx/dt)

Given that dA/dt = 24 cm^2/min, we can find dx/dt when A = 169 cm^2 (which is the area of a square with side length of 13 cm):

24 = 2(13)(dx/dt)

Simplifying this expression, we get:

dx/dt = 24/(26) = 12/13

Therefore, the length of the edge of the square is increasing at a rate of 12/13 cm/min when the area is 169 cm^2.

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_____The given question is incomplete, the complete question is given below:

The area of a square is increasing at a rate of 24 cm^2/min

How fast is the length of the edge increasing when the area = 64 cm^2

The car is depreciating by about 0.68% every quarter.

Quarterly rate is a financial term that refers to the interest rate applied to a loan or investment that compounds every quarter, or every three months.

Let f(t) represent the car's worth after t years. We can write a function to represent the value of the car after t years as follows:

f(t) = 10000(1 - 0.18/4)[tex]^(4t)[/tex]

In this function, the quarterly rate of change is 0.18/4 = 0.045. The value of the car is depreciating by 4.5% every quarter.

To determine the percentage rate of change per quarter to the nearest hundredth of a percent, we can use the formula:

r = [tex](1 - q)^4[/tex] - 1

where q is the quarterly rate of change (0.045 in this case) and r is the percentage rate of change per quarter.

Plugging in the values, we get:

r = [tex](1 - 0.045)^4[/tex] - 1

r ≈ -0.68%

So the car is depreciating by about 0.68% every quarter.

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A mathematical process called subtraction reflects the elimination of items from a collection. There are 14 pupils that enjoy pink polka dots.

A mathematical process called subtraction reflects the elimination of items from a collection.

Subtraction is symbolised by the negative sign.

Considering that there were 50 students in the sample as a whole, the number of pupils who enjoy pink polka dots is as follows:

50 students divided by (4+9+11+9+3) yields 14 students.

Thus, there are 14 students that enjoy pink polka dots.

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The complete question is:

A sample of 50 11th graders was asked to select a favorite pattern out of 6 choices. the following display shows what their favorite color patterns were.

blue on grey 4

green 9

pink polka dots?

purple 11

red and orange stripes 9

yellow 3

The counts have been recorded in the accompanying table according to pattern and the number of students who selected the pattern. what is the missing value in the table?

The reflection's rule is described below. The right response is x-axis (x, y) = (x, -y).

When we gaze at our own reflection in a mirror, we naturally think of a reflection as a mirror image.

In maths, the concept of reflection and a mirror image are comparable.

The rules for reflection across the y-axis and x-axis are fundamental transformations in geometry. The rule for reflection across the y-axis is (x, y) → (-x, y), which means that every point's x-coordinate is negated while the y-coordinate remains the same. This transformation has the effect of reflecting the object or figure across the y-axis.    

Similarly, the rule for reflection across the x-axis is (x, y) → (x, -y), which means that every point's y-coordinate is negated while the x-coordinate remains the same. This transformation has the effect of reflecting the object or figure across the x-axis. These transformations are important in many areas of mathematics and science, including computer graphics and physics.

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The table of values of the equation y = -4x is

x y

-2 8

-1 4

0 0

1 -4

Given that

y = -4x

To find the values that complete the table for the given equation y=-4x, we substitute each value of x and evaluate y.

When x = -2, y = -4x = -4(-2) = 8

When x = -1, y = -4x = -4(-1) = 4

When x = 0, y = -4x = -4(0) = 0

When x = 1, y = -4x = -4(1) = -4

So the completed table is:

x y

-2 8

-1 4

0 0

1 -4

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The reasons that completes the proof to show that WX ≅ ZY are:

2. Given; 3. Alternate Interior Angles Theorem 4. Reflexive Property of Congruence 5. AAS 6. CPCTC.

Given that WX║ZY and <X ≅ <Z, we can prove that WX ≅ ZY as shown below in the proof.

Statements                        Reasons                                          

1. WX║ZY                          1. Given

2. <X ≅ <Z                         2. Given

3. <XWY ≅ <ZYW              3.  Alternate Interior Angles Theorem

4. WY ≅ WY                      4. Reflexive Property of Congruence

5. ΔWZY ≅ ΔYXW            5. AAS

6. WX ≅ ZY                       6. CPCTC

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The average rate of change of the function f(x) from x = 2 to x = 6 is 13.

In mathematics, a function is a rule that associates each element of a set (called the domain) with a unique element in another set (called the range). In other words, a function is a relationship between two sets, where each element of the domain is paired with exactly one element in the range.

To find the average rate of change of the function f(x) from x=2 to x=6, we need to calculate the slope of the secant line between the two points.

The formula for the average rate of change of a function f(x) from x=a to x=b is:

average rate of change = (f(b) - f(a)) / (b - a)

In this case, a = 2 and b = 6. So we have:

average rate of change = (f(6) - f(2)) / (6 - 2)

Now, let's substitute the values of f(6) and f(2) in the above equation:

average rate of change = ((6)² + 5(6) - 8 - (2)² - 5(2) + 8) / (6 - 2)

average rate of change = (36 + 30 - 8 - 4 - 10 + 8) / 4

average rate of change = 52 / 4

average rate of change = 13

Therefore, the average rate of change of the function f(x) from x = 2 to x = 6 is 13.

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